Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous activity, the network displays orderly, perfectly synchronized periodic responses at intermediate level of noise. We show that this phenomenon is fundamentally stochastic and collective in nature. Indeed, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited neurons eventually triggering a chain reaction associated with a macroscopic synchronized excursion and a collective return to rest where this process starts afresh, thus yielding the observed periodic synchronized oscillations. We further uncover a novel anti-resonance phenomenon: noise-induced synchronized oscillations disappear when the system is driven by periodic stimulation with frequency within a specific range. In that anti-resonance regime, the system is optimal for measures of information capacity. This observation provides a new hypothesis accounting for the efficiency of Deep Brain Stimulation therapies in Parkinson's disease, a neurodegenerative disease characterized by an increased synchronization of brain motor circuits. We further discuss the universality of these phenomena in the class of stochastic networks of excitable elements with confining coupling, and illustrate this universality by analyzing various classical models of neuronal networks. Altogether, these results uncover some universal mechanisms supporting a regularizing impact of noise in excitable systems, reveal a novel anti-resonance phenomenon in these systems, and propose a new hypothesis for the efficiency of high-frequency stimulation in Parkinson's disease

New Insights into the Spinal Recurrent Inhibitory Pathway Normally and After Motoneuron Regeneration

Despite more than seven decades of intensive research, uncertainty is the hallmark of spinal recurrent inhibition. The simplest possible structure that is formed between the a-motoneuron and its inhibitory interneurons has been the subject of long lasting scientific debate. To date, there is no consensus on the functional significance of this circuit. Even the simplest assumption of a negative feedback loop does not hold true. The current work used the technique of in vivo intracellular recording from the adult rat a-motoneurons to study the normal function and the plasticity after nerve injury and regeneration of this simple, yet intricate spinal circuit. The long lasting notion that inhibition must adversely affect neuronal firing rates has been challenged and the counter-intuitive finding that recurrent inhibition can increase firing rate under certain circumstances is reported for the first time. In addition, recurrent inhibition was found to strongly affect action potential spike timing and was found to prolong the duration of repetitive firing of a-motoneurons. Furthermore, the circuit behavior at different frequencies has been examined and novel findings are reported. The circuit adaptation to peripheral nerve injury and successful regeneration was studied. Results showed that peripheral nerve regeneration failed to restore the structure and function of this central circuit. In conclusion, the current thesis calls for a reevaluation of the concept that recurrent inhibition must suppress a-motoneuron firing and suggests that inhibition in general plays more of a role in modulating firing behavior. Finally, another example of permanent central nervous system dysfunction despite successful peripheral recovery is reported and perhaps adds to the permanent functional deficits that remain in victims of peripheral nerve injury

Shared inputs, entrainment, and desynchrony in elliptic bursters: from slow passage to discontinuous circle maps

What input signals will lead to synchrony vs. desynchrony in a group of biological oscillators? This question connects with both classical dynamical systems analyses of entrainment and phase locking and with emerging studies of stimulation patterns for controlling neural network activity. Here, we focus on the response of a population of uncoupled, elliptically bursting neurons to a common pulsatile input. We extend a phase reduction from the literature to capture inputs of varied strength, leading to a circle map with discontinuities of various orders. In a combined analytical and numerical approach, we apply our results to both a normal form model for elliptic bursting and to a biophysically-based neuron model from the basal ganglia. We find that, depending on the period and amplitude of inputs, the response can either appear chaotic (with provably positive Lyaponov exponent for the associated circle maps), or periodic with a broad range of phase-locked periods. Throughout, we discuss the critical underlying mechanisms, including slow-passage effects through Hopf bifurcation, the role and origin of discontinuities, and the impact of noiseComment: 17 figures, 40 page

Determining how stable network oscillations arise from neuronal and synaptic mechanisms

Many animal behaviors involve the generation of rhythmic patterns and movements. These rhythmic patterns are commonly mediated by neural networks that produce an oscillatory activity pattern, where different neurons maintain a relative phase relationship. This thesis examines the relationships between the cellular and synaptic properties that give rise to stable activity in the form of phase maintenance, across different frequencies in a well-suited model system, the pyloric network of the crab Cancer borealis. The pyloric network has endogenously oscillating ‘pacemaker’ neurons that inhibit ‘follower’ neurons, which in turn feed back onto the pacemaker neurons. The focus of this thesis was to determine the methods by which phase maintenance is achieved in an oscillatory network. This thesis examines the idea that phase maintenance occurs through the actions of intrinsic properties of isolated neurons or through the dynamics of their synaptic connections or both. A combination of pharmacological and electrophysiological techniques a used to show how identified membrane properties and short-term synaptic plasticity are involved with phase maintenance over a range of biologically relevant oscillation frequencies. To examine whether network stability is due to the characteristic stable activity of the identified pyloric neuron types, the hypothesis that phase maintenance is an inherent property of synaptically-isolated individual neurons in the pyloric network was first tested. A set of parameters were determined (frequency-dependent activity profile) to define the response of each isolated pyloric neuron to sinusoidal input at different frequencies. The parameters that define the activity profile are: burst onset phase, burst end phase, resonance frequency and intra-burst spike frequency. Each pyloric neuron type was found to possess a unique activity profile, indicating that the individual neuron types are tuned to produce a particular activity pattern at different frequencies depending on their role in the network. To elucidate the biophysical properties underlying the frequency-dependent activity profiles of the neurons, the hyperpolarization activated current (Ih) was measured and found to possess frequency-dependent properties. This implies that Ih has a different influence on the activity phase of pyloric neurons at different frequencies. Additionally, it was found that the Ih contribution to the burst onset phase depends on the neuron type: in the pacemaker group neurons (PD) it had no influence on the burst onset phase at any frequency whereas in follower neurons it acted to advance the onset phase in one neuron type (LP) and, paradoxically, to delay it in a different neuron type (PY). The results from this part of the study provided evidence that stability is due in part to the intrinsic neuronal properties but that these intrinsic properties do not fully explain network stability. To address the contribution of pyloric synapses to network stability, the mechanisms by which synapses promote phase maintenance were investigated. An artificial synapse that mimicked the feedforward PD to LP synapse, was used so that the synaptic parameters could be varied in a controlled manner in order to examine the influence of the properties of this synapse on the postsynaptic LP neuron. It was found that a static synapse with fixed parameters (such as strength and peak phase) across frequencies cannot result in a constant activity phase in the LP neuron. However, if the synaptic strength decreases and the peak phase is delayed as a function of frequency, the LP neuron can maintain a constant activity phase across a large range of frequencies. These dynamic changes in the strength and peak phase of the PD to LP synapse are consistent with the short-term plasticity properties previously reported for this synapse. In the pyloric network, the follower neuron LP provides the sole transmitter-mediated feedback to the pacemaker neurons. To understand the role of this synapse in network stability, this synapse was blocked and replaced by an artificial synapse using the dynamic clamp technique. Different parameters of the artificial synapse, including strength, peak phase, duration and onset phase were found to affect the pyloric cycle period. The most effective parameters that influence cycle period were the synaptic duration and its onset phase. Overall this study demonstrated that both the intrinsic properties of individual neurons and the dynamic properties of the synapses are essential in producing stable activity phases in this oscillatory network. The insight obtained from this thesis can provide a general understanding of the contribution of intrinsic properties to neuronal activity phase and how short-term synaptic dynamics can act to promote phase maintenance in oscillatory networks

Elucidating the Interplay of Structure, Dynamics, and Function in the Brain’s Neural Networks.

Brain’s structure, dynamics, and function are deeply intertwined. To understand how the brain functions, it is crucial to uncover the links between network structure and its dynamics. Here I examine different approaches to exploring the key connecting factors between network structure, dynamics and eventually its function. I predominantly concentrate on emergence and temporal evolution of synchronization, or coincidence of neuronal spike timings, as it has been associated with many brain functions while aberrant synchrony is implicated in many neurological disorders. Specifically, in chapter II, I investigate how the interplay of cellular properties with network coupling characteristics could affect the propensity of neural networks for synchronization. Then, in chapter III, I develop a set of measures that identify hallmarks and potentially predict autonomous network transitions from asynchronous to synchronous dynamics under various conditions. The developed metrics can be calculated in real time and therefore potentially applied in clinical situations. Finally, in chapter IV, I aim to tie the correlates of neural network dynamics to the brain function. More specifically, I elucidate dynamical underpinnings of learning and memory consolidation from in vivo recordings of mice experiencing contextual fear conditioning (CFC) and show, that the introduced notion of network stability may predict future animal performance on memory retrieval. Overall, the results presented within this dissertation underscore the importance of concurrent analysis of networks’ dynamical and structural properties. The developed approaches may prove useful beyond the specific application presented within this thesis.PhDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120768/1/mofakham_1.pd

Mechanical Control of Sensory Hair-Bundle Function

Hair bundles detect sound in the auditory system, head position and rotation in the vestibular system, and fluid flow in the lateral-­‐‑line system. To do so, bundles respond to periodic, static, and hydrodynamic forces contingent upon the receptor organs in which they are situated. As the mechanosensory function of a hair bundle varies, so too do the mechanical properties of the bundle and its microenvironment. Hair bundles range in height from 1 μμm to 100 μμm and in stiffness from 100 μμN·∙m-­‐‑1 to 10,000 μμN·∙m-­‐‑1. They are composed of actin-­‐‑filled, hypertrophic microvilli—stereocilia—that number from fewer than 20 through more than 300 per bundle. In addition, bundles may or may not possess one true cilium, the kinocilium. Hair bundles differ in shape across organs and organisms: they may be isodiametric, fan-­‐‑shaped, or V-­‐‑shaped. Depending on the organ in which they occur, bundles may be free-­‐‑standing or they may be coupled to a tectorial membrane, otolithic membrane, cupula, or sallet. Because all hair bundles are comprised of similar molecular components, their distinct mechanosensory functions may instead be regulated by their mechanical loads. Dynamical-­‐‑systems analysis provides mathematical predictions of hair-­‐‑bundle behavior. One such model captures the effects of mechanical loading on bundle function in a state diagram. A mechanical-­‐‑load clamp permits exploration of this state diagram by robustly controlling the loads—constant force, load stiffness, virtual drag, and virtual mass—imposed on a hair bundle. Upon changes in these mechanical parameters, the bundle’s response characteristics alter. Subjected to particular control parameters, a bundle may oscillate spontaneously or remain quiescent. It may respond nonlinearly to periodic stimuli with high sensitivity, sharp frequency tuning, and easy entrainment; or it may respond linearly with low sensitivity, broad tuning, and reluctant entrainment. The bundle’s response to a force pulse may resemble that of an edge-­‐‑detection system or a low-­‐‑pass filter. Finally, a bundle from an amphibian vestibular organ can operate in a manner qualitatively similar to that from a mammalian auditory organ, implying an essential similarity between hair bundles. The bifurcation near which a bundle’s operating point resides controls its function: the state diagram provides a functional map of mechanosensory modalities. Auditory function is best tuned near a supercritical Hopf bifurcation, whereas vestibular function is captured by a subcritical Hopf bifurcation and a cusp bifurcation. Within the proposed region vestibular responsiveness, a hair bundle exhibits mechanical excitability analogous to the electrical excitability of neurons. This behavior implies for the first time a direct relationship between the mechanical behaviors of sensory organelles and the electrical behaviors of afferent neurons. Man-­‐‑made detectors function in limited capacities, each designed for a unique purpose. A single hair bundle, on the other hand, evolved to serve multiple purposes with the requirement of only two functional traits: adaptation and nonlinear channel gating. The remarkable conservation of these capabilities thus provides unique insight into the evolution of sensory systems

Quantum materials for energy-efficient neuromorphic computing

Neuromorphic computing approaches become increasingly important as we address future needs for efficiently processing massive amounts of data. The unique attributes of quantum materials can help address these needs by enabling new energy-efficient device concepts that implement neuromorphic ideas at the hardware level. In particular, strong correlations give rise to highly non-linear responses, such as conductive phase transitions that can be harnessed for short and long-term plasticity. Similarly, magnetization dynamics are strongly non-linear and can be utilized for data classification. This paper discusses select examples of these approaches, and provides a perspective for the current opportunities and challenges for assembling quantum-material-based devices for neuromorphic functionalities into larger emergent complex network systems